A revisit of the k-space filtering effects of magnetization-prepared 3D FLASH and balanced SSFP acquisitions: Analytical characterization of the point spread functions

Purpose: 3D FLASH and balanced SSFP (bSSFP) are increasingly used in quantitative MRI after contrast preparation. The acquired k-space data are modulated by T₁ relaxation (or additional T₂ for bSSFP). Three separate sequence parameters including the number of phase-encoding steps per shot (N), flip angle (FA), and TR have made the transient state of rapid gradient echo (GRE) imaging difficult for analysis and optimization. Here we aim to analytically characterize the k-space filtering effect of magnetization-prepared FLASH and bSSFP with the point spread functions (PSF). Methods: The amplitude effect is characterized with the peak magnitude of the PSF, i.e. PSF(0), which, due to their approaching from transient state to steady-state for the GRE acquisitions, obeys a linear (with a slope and an intercept, not proportional) relationship with the prepared longitudinal magnetization (M_prep). The blurring effect is characterized by the FWHM of the PSF. The magnetization-prepared acquisition-dependent image contrast efficiency is characterized with the relative contrast-to-noise ratio (CNR) per unit time (ruCNR). Results: The slope of PSF(0) characterizes the relative contrast between different M_prep levels. The intercept of PSF(0) could lead to quantification bias for magnetization-prepared imaging. FLASH and bSSFP experience very little blurring effect, which is to the contrary of conventional fast spin echo (FSE). Analytical selections of N, FA, and TR are provided to optimize ruCNR for different scenarios. Conclusions: PSFs of the FLASH and bSSFP acquisitions are analytically derived and numerically validated, and compared with the FSE acquisition, thus providing a useful tool for optimizing magnetization-prepared GRE acquisitions.